Below is the diamgram of the region.Originally Posted byJaysFan31

In order to solve this problem you need to find thecountinous density function. Which you say is proportional to the distance. I take this to mean that you are sayingdirectly proportionalright? Then you have,

for some constant of proportionality.

In mathematical terms,

Thus,

In order to find the center of mass you first need to find the mass. Which in this case is,

Thus,

I believe it is easier by converting to polar cordinates.

Thus,

Thus,

--->Mass

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I will continue later.